! ! Parallel Sparse BLAS version 3.5 ! (C) Copyright 2006-2018 ! Salvatore Filippone ! Alfredo Buttari ! ! Redistribution and use in source and binary forms, with or without ! modification, are permitted provided that the following conditions ! are met: ! 1. Redistributions of source code must retain the above copyright ! notice, this list of conditions and the following disclaimer. ! 2. Redistributions in binary form must reproduce the above copyright ! notice, this list of conditions, and the following disclaimer in the ! documentation and/or other materials provided with the distribution. ! 3. The name of the PSBLAS group or the names of its contributors may ! not be used to endorse or promote products derived from this ! software without specific written permission. ! ! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR ! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS ! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR ! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF ! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS ! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN ! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! ! ! File: psb_dfcg.f90 !! !! Contributors: Ambra Abdullahi (UNITOV) and Pasqua D’Ambra (IAC-CNR) !! ! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! C C ! C References: C ! C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C ! C Level 3 basic linear algebra subprograms for sparse C ! C matrices: a user level interface C ! C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C ! C C ! C C ! C [2] S. Filippone, M. Colajanni C ! C PSBLAS: A library for parallel linear algebra C ! C computation on sparse matrices C ! C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C ! C C ! C [3] M. Arioli, I. Duff, M. Ruiz C ! C Stopping criteria for iterative solvers C ! C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C ! C C ! C C ! C [4] R. Barrett et al C ! C Templates for the solution of linear systems C ! C SIAM, 1993 ! C C ! C [4] Notay, Yvan C ! C Flexible Conjugate gradients C ! C SIAM Journal on Scientific Computing 22(4), C ! C pp. 1444-1460, 2000 C ! C C ! C C ! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_dfcg.f90 ! ! Subroutine: psb_dfcg ! This subroutine implements the Flexible Conjugate Gradient method. ! ! ! Arguments: ! ! a - type(psb_dspmat_type) Input: sparse matrix containing A. ! prec - class(psb_dprec_type) Input: preconditioner ! b(:) - real Input: vector containing the ! right hand side B ! x(:) - real Input/Output: vector containing the ! initial guess and final solution X. ! eps - real Input: Stopping tolerance; the iteration is ! stopped when the error estimate |err| <= eps ! desc_a - type(psb_desc_type). Input: The communication descriptor. ! info - integer. Output: Return code ! ! itmax - integer(optional) Input: maximum number of iterations to be ! performed. ! iter - integer(optional) Output: how many iterations have been ! performed. ! performed. ! err - real (optional) Output: error estimate on exit. If the ! denominator of the estimate is exactly ! 0, it is changed into 1. ! itrace - integer(optional) Input: print an informational message ! with the error estimate every itrace ! iterations ! istop - integer(optional) Input: stopping criterion, or how ! to estimate the error. ! 1: err = |r|/(|a||x|+|b|); here the iteration is ! stopped when |r| <= eps * (|a||x|+|b|) ! 2: err = |r|/|b|; here the iteration is ! stopped when |r| <= eps * |b| ! where r is the (preconditioned, recursive ! estimate of) residual. ! ! subroutine psb_dfcg_vect(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop,cond) use psb_base_mod use psb_prec_mod use psb_d_krylov_conv_mod use psb_krylov_mod implicit none type(psb_dspmat_type), intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a class(psb_dprec_type), intent(inout) :: prec type(psb_d_vect_type), Intent(inout) :: b type(psb_d_vect_type), Intent(inout) :: x real(psb_dpk_), Intent(in) :: eps integer(psb_ipk_), intent(out) :: info integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, istop integer(psb_ipk_), Optional, Intent(out) :: iter real(psb_dpk_), Optional, Intent(out) :: err,cond ! = Local data type(psb_d_vect_type) :: v, w, d , q, r real(psb_dpk_) :: alpha, beta, delta, gamma, theta real(psb_dpk_) :: derr integer(psb_ipk_) :: i, idx, nc2l, it, itx, istop_, itmax_, itrace_ integer(psb_ipk_) :: n_col, naux, err_act integer(psb_lpk_) :: mglob integer(psb_ipk_) :: debug_level, debug_unit type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: np, me real(psb_dpk_), allocatable, target :: aux(:) real(psb_dpk_) :: vres(3) character(len=20) :: name type(psb_itconv_type) :: stopdat character(len=*), parameter :: methdname='FCG' logical, parameter :: debug = .false. info = psb_success_ name = 'psb_dfcg' call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ctxt = desc_a%get_context() call psb_info(ctxt, me, np) if (.not.allocated(b%v)) then info = psb_err_invalid_vect_state_ call psb_errpush(info,name) goto 9999 endif if (.not.allocated(x%v)) then info = psb_err_invalid_vect_state_ call psb_errpush(info,name) goto 9999 endif mglob = desc_a%get_global_rows() n_col = desc_a%get_local_cols() if (present(istop)) then istop_ = istop else istop_ = 2 endif call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info) if (info == psb_success_)& & call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on X/B') goto 9999 end if naux=4*n_col allocate(aux(naux), stat=info) if (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if !Assemble w, v, d, q, r, u call psb_geasb(w, desc_a,info,& & scratch=.true.,mold=x%v) call psb_geasb(v, desc_a,info,& & scratch=.true.,mold=x%v) call psb_geasb(d, desc_a,info,& & scratch=.true.,mold=x%v) call psb_geasb(q, desc_a,info,& & scratch=.true.,mold=x%v) call psb_geasb(r, desc_a,info,& & scratch=.true.,mold=x%v) call psb_init_conv(methdname,istop_,itrace_,itmax_,& & a,x,b,eps,desc_a,stopdat,info) itx = 0 restart: do if (itx>= itmax_) then if (debug.and.(me==0)) write(0,*) name,' Exit on itmax ' exit restart end if ! r=b -Ax call psb_geaxpby(done,b,dzero,r, desc_a,info) if (info == psb_success_) call psb_spmm(-done,a,x,done,r,desc_a,info) if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,& & a_err='Error during residual') goto 9999 end if if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) then if (debug.and.(me==0)) write(0,*) name,' Exit on convergence from restart' exit restart end if ! Apply the preconditioner v=Pr ! Compute w = Av call prec%apply(r,v,desc_a,info,work=aux) if (info == psb_success_) call psb_spmm(done,a,v,dzero,w,desc_a,info) if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,& & a_err='Error during residual') goto 9999 end if vres(1) = psb_gedot(r, v, desc_a, info, global = .false.) vres(2) = psb_gedot(w, v, desc_a, info, global = .false.) call psb_sum(ctxt, vres(1:2)) alpha = vres(1) beta = vres(2) if (debug.and.(me==0)) then write(0,*) name,' restart AB',itx, alpha, beta end if if (beta == dzero) then if (debug.and.(me==0)) write(0,*) name,' Exit on beta=0 from restart' exit restart end if ! d = v call psb_geaxpby(done, v, dzero, d, desc_a, info) ! q = w call psb_geaxpby(done, w, dzero, q, desc_a, info) ! compute delta=beta ! then ! x = x + (alpha/delta)*d ! r = r - (alpha/delta)*q ! DELTA==0 here would have been caught earlier delta = beta theta = alpha/delta call psb_geaxpby(theta, d, done, x, desc_a, info) call psb_geaxpby(-theta, q, done, r, desc_a, info) if (debug.and.(me==0)) then write(0,*) name,' restart DT',itx, delta, theta end if iteration: do itx = itx + 1 if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) then if (debug.and.(me==0)) write(0,*) name,' Exit on convergence from iteration' exit restart end if ! Apply the preconditioner v = Pr ! Compute w = Av call prec%apply(r,v,desc_a,info,work=aux) if (info == psb_success_) call psb_spmm(done,a,v,dzero,w,desc_a,info) if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,& & a_err='Error during residual'); goto 9999 end if vres(1) = psb_gedot(r, v, desc_a, info, global = .false.) vres(2) = psb_gedot(w, v, desc_a, info, global = .false.) vres(3) = psb_gedot(q, v, desc_a, info, global = .false.) call psb_sum(ctxt, vres(1:3)) alpha = vres(1) beta = vres(2) gamma = vres(3) ! Compute d = v-(gamma/delta)*d ! q = w-(gamma/delta)*q ! DELTA==0 here would have been caught earlier theta= gamma/delta call psb_geaxpby(done, v, -theta, d, desc_a, info) call psb_geaxpby(done, w, -theta, q , desc_a, info) ! update delta delta = beta - (gamma*gamma)/delta if (delta == dzero) then if (debug.and.(me==0)) write(0,*) name,' Exit on delta=0 from iteration' exit iteration end if ! update u and r ! u = u + (alpha/delta)*d ! r = r - (alpha/delta)*q theta= alpha/delta if (debug.and.(me==0)) then write(0,*) name,' iteration ',itx, alpha,beta,gamma,delta,theta end if call psb_geaxpby(theta, d, done, x, desc_a, info) call psb_geaxpby(-theta, q, done, r, desc_a, info) end do iteration end do restart call psb_end_conv(methdname,itx ,desc_a,stopdat,info,derr,iter) if (present(err)) err = derr return 9999 continue call psb_erractionrestore(err_act) if (err_act.eq.psb_act_abort_) then call psb_error() return end if return end subroutine psb_dfcg_vect